He sort of became an apprentice to a rakugo comedian (traditional Japanese comedy), who's called Tsukitei something. Apprentices in the traditional Japanese arts generally inherit the surname of their master for their stage name. In this case, "Tsukitei".

I'm not entirely sure why Yamazaki/tsukitei suddenly began rakugo. From what I've gathered, he wasn't very confident in his own ability and future as an ordinary comedian, wanted to explore new avenues, skills etc, and so tried out rakugo. Apparently he's pretty good at it though.